The simplest way to solve these problems is to give the agency or person exactly what they request. You're overthinking it. If you follow instructions and provide the correct information, the fact that the interviewer might have made a "mistake" is irrelevant. The people you come into contact with are just trying to do their jobs. You can't change how they feel about something, but you can give them the correct information. Give them exactly what they ask for. There's nothing to be confused about. It works every time.